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st: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model

From   Sachin Chintawar <>
Subject   st: Re: Monte Carlo Simulation for Heteroskedastic Tobit Model
Date   Thu, 16 Apr 2009 15:41:06 -0600

Dear all
Thank you Martin & other statalist users

Well I did find the book very helpful. Find a program that I have been
able to now develop. But has a few problems
clear all

quietly set obs 30
global numobs 100             // sample size N
global numsims "1000"         // number of simulations
set seed 678643594

program tobit, rclass
 version 10.1
 drop _all
 set obs $numobs
 scalar a = 0
 scalar b = 12
 scalar mu = 5
 scalar sigma = 4
 generate u= runiform()
generate y=normal((a-mu)/sigma)+u*(normal((b-mu)/sigma)-normal((a-mu)/sigma))
generate ytrunc = mu + sigma*invnorm(y)
 generate x = rnormal()

 regress ytrunc x
 return scalar b2 = _b[x]
 return scalar se2 = _se[x]
 return scalar t2 = (_b[x]-2)/_se[x]
 return scalar r2 = abs(return(t2))> invttail($numobs-2,.025)
 return scalar p2 = 2*ttail($numobs-2,abs(return(t2)))

 simulate b2r=r(b2) se2r=r(se2) t2r=r(t2) reject2r=r(r2) p2r=r(p2), ///
	reps($numsims): tobit
mean b2r se2r reject2r

My Questions now are:
1. Since I had generated 'ytrunc' as a truncated normal distribution,
then to know the bias I cannot tell stata to generate 'ytrunc' based
on a equation such as
         y = b1 + b2*x + u
     where b1 and b2 are specified. But if I do this then y goes to
having a normal distribution and not a truncated normal distribution.

2. Another problem is to develop a heteroskedastic error term. Can I
develop that using
           generate u= runiform() * c*z_factor

             Where c is a constant varying from 0.1 to 1.0 and the
z_factor changes for each 'i' - then how do I define the z_factor?

I would greatly appreciate any pointers that you could provide me in this regard

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